NonCommutativeExpand
NonCommutativeExpand[expr,alg]
expands out the non-commutative algebra alg operations in expr.
Details
- NonCommutativeExpand is typically used to expand out non-commutative algebra operations.
- NonCommutativeExpand expands out the algebra multiplication with respect to the algebra addition. The multiplication and addition operations are specified in alg.
- alg can be a NonCommutativeAlgebra object, {Dot,n}, Composition, TensorProduct or NonCommutativeMultiply. If the algebra argument is omitted, NonCommutativeAlgebra with the default property values is used.
- Positive integer powers of the algebra multiplication operation mult are expressed using GeneralizedPower, where GeneralizedPower[mult,e,2]==mult[e,e] and GeneralizedPower[mult,e,k+1]==mult[GeneralizedPower[mult,e,k],e].
- NonCommutativeExpand threads over lists in the first argument.
Examples
open all close allBasic Examples (4)
Expand NonCommutativeMultiply with respect to Plus:
Expand out multiplication mult with respect to addition add:
Specify that the variable c commutes with all algebra elements:
Scope (6)
Expand GeneralizedPower of a sum:
Square matrices with Dot product form an algebra:
Linear endomorphisms with Composition form an algebra:
Expand polynomials over an abstract algebra with symbolic property names:
Scalar arguments to algebra operations are interpreted as scalar multiples of the multiplicative unity:
NonCommutativeExpand threads over lists in the first argument:
Applications (1)
Properties & Relations (1)
NonCommutativeExpand expands out the algebra multiplication with respect to the algebra addition:
Expand expands out Times with respect to Plus:
ArrayExpand expands out array operations:
Possible Issues (1)
NonCommutativeExpand works over a free algebra, without recognizing any relations between variables:
ArrayExpand recognizes the relations between a matrix and its inverse:
Text
Wolfram Research (2025), NonCommutativeExpand, Wolfram Language function, https://reference.wolfram.com/language/ref/NonCommutativeExpand.html.
CMS
Wolfram Language. 2025. "NonCommutativeExpand." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NonCommutativeExpand.html.
APA
Wolfram Language. (2025). NonCommutativeExpand. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NonCommutativeExpand.html